Tolerance Analysis Method Using Improved Convolution Method

2012 ◽  
Vol 271-272 ◽  
pp. 1463-1466
Author(s):  
Shao Gang Liu ◽  
Qiu Jin
Keyword(s):  
Linear Dimension ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Analysis Methods ◽  
Statistical Tolerance ◽  
Nonlinear Dimension ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

Convolution method is studied to analyze statistical tolerance for linear dimension chain and nonlinear dimension chain. Hybrid convolution method is proposed, which is the integration of analytical convolution and numerical convolution. In order to reduce the algorithm errors, improved convolution method is proposed. Comparing with other statistical tolerance analysis methods, this method is faster and accurate. At last, an example is used to demonstrate the method proposed in this paper.

NON-NORMAL STATISTICAL TOLERANCE ANALYSIS USING ANALYTICAL CONVOLUTION METHOD

2008 ◽  
Vol 07 (01) ◽  
pp. 127-130 ◽  
Author(s):  
S. G. LIU ◽  
P. WANG ◽  
Z. G. LI
Keyword(s):  
Normal Distribution ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Accurate Method ◽  
Probability Density Functions ◽  
Triangular Distribution ◽  
Normal Distributions ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

In statistical tolerance analysis, it is usually assumed that the statistical tolerance is normally distributed. But in practice, there are many non-normal distributions, such as uniform distribution, triangular distribution, etc. The simple way to analyze non-normal distributions is to approximately represent it with normal distribution, but the accuracy is low. Monte-Carlo simulation can analyze non-normal distributions with higher accuracy, but is time consuming. Convolution method is an accurate method to analyze statistical tolerance, but there are few reported works about it because of the difficulty. In this paper, analytical convolution is used to analyze non-normal distribution, and the probability density functions of closed loop component are obtained. Comparing with other methods, convolution method is accurate and faster.

A Nonlinear Tolerance Analysis Method Using Worst-Case and Matlab

2011 ◽  
Vol 201-203 ◽  
pp. 247-252
Author(s):  
Mei Qiong Yu ◽  
Yan Yan ◽  
Jia Hao ◽  
Guo Xin Wang
Keyword(s):  
Mathematical Formulation ◽  
Tolerance Analysis ◽  
Worst Case Analysis ◽  
Analysis Method ◽  
Worst Case ◽  
Analysis Methods ◽  
Precision Design ◽  
Basic Parameters ◽  
Statistical Tolerance ◽  
Production Requirement

The tolerance analysis methods are usually used to test the result of product design and assembly; moreover the tolerance analysis also is a fundamental technique in precision design process. So far, there are two kinds of tolerance analysis methods: statistical tolerance analysis and worst-case analysis; they have their own characteristics and drawbacks. In this paper, it presents a nonlinear tolerance analysis method which uses Matlab tool to construct the nonlinear tolerance analysis mathematical formulation and calculate the result of nonlinear tolerance analysis based on the principle of worst-case tolerance analysis. All the processes are dealt with and tested by computer. The engineers only enter some basic parameters through the standardized interface, and then the result can be obtained without artificial intervention. In addition, the accuracy of calculation result meets the production requirement. The system of the nonlinear tolerance analysis is easier for engineers to use.

A Statistical Tolerance Analysis Method for Feature in Non-Normal Distribution

2010 ◽  
Author(s):  
Chang-Hsin Kuo ◽  
Jhy-Cherng Tsai
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Normal Distribution ◽  
Mechanical Design ◽  
Tolerance Analysis ◽  
Analysis Method ◽  
Normal Distributions ◽  
Tolerance Specification ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

The tolerance analysis of an assembly is an important issue for mechanical design. Among many tolerance analysis methods, the conventional statistical tolerance analysis method is the most popular one. However, the conventional statistical tolerance analysis method is based on the normal distribution. It fails to predict the resultant tolerance of an assembly with features in non-normal distributions. In this paper, the distributions of features are transferred into statistical moments first. Then, the tolerance stack-up can be handled based on these moments. Finally, the computed resultant moments can be mapped back to probability distribution to find the resultant tolerance specification of the assembly. Two examples are used to demonstrate the proposed method. Compared to the resultants by Monte Carlo simulation with 1,000,000 samples, the predicted resultant tolerance specifications by this method are only −0.868% and 0.799% differences. The predicted resultant tolerances of this method are fast and accurate.

scholarly journals Tolerance Analysis of Over-Constrained Assembly Considering Gravity Influence: Constraints of Multiple Planar Hole-Pin-Hole Pairs

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Xia Liu ◽  
Luling An ◽  
Zhiguo Wang ◽  
Changbai Tan ◽  
Xiaoping Wang
Keyword(s):  
Coupling Effect ◽  
Tolerance Analysis ◽  
Physical Factors ◽  
Analysis Method ◽  
Mechanical Joints ◽  
Propagation Analysis ◽  
Deviation Propagation ◽  
Minimum Potential ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Over-constrained assembly of rigid parts is widely adopted in aircraft assembly to yield higher stiffness and accuracy of assembly. Unfortunately, the quantitative tolerance analysis of over-constrained assembly is challenging, subject to the coupling effect of geometrical and physical factors. Especially, gravity will affect the geometrical gaps in mechanical joints between different parts, and thus influence the deviations of assembled product. In the existing studies, the influence of gravity is not considered in the tolerance analysis of over-constrained assembly. This paper proposes a novel tolerance analysis method for over-constrained assembly of rigid parts, considering the gravity influence. This method is applied to a typical over-constrained assembly with constraints of multiple planar hole-pin-hole pairs. This type of constraints is non-linear, which makes the tolerance analysis more challenging. Firstly, the deviation propagation analysis of an over-constrained assembly is conducted. The feasibility of assembly is predicted, and for a feasible assembly, the assembly deviations are determined with the principle of minimum potential energy. Then, the statistical tolerance analysis is performed. The probabilities of assembly feasibility and quality feasibility are computed, and the distribution of assembly deviations is estimated. Two case studies are presented to show the applicability of the proposed method.

Statistical Tolerance Analysis With Sensitivities Established With Tolerance-Maps

2018 ◽  
Author(s):  
Aniket N. Chitale ◽  
Joseph K. Davidson ◽  
Jami J. Shah
Keyword(s):  
Tolerance Analysis ◽  
Minkowski Sum ◽  
Coordinate Frame ◽  
Target Feature ◽  
Functional Feature ◽  
Design Function ◽  
Statistical Tolerance ◽  
The One ◽  
The Relationship ◽  
Statistical Tolerance Analysis

The purpose of math models for tolerances is to aid a designer in assessing relationships between tolerances that contribute to variations of a dependent dimension that must be controlled to achieve some design function and which identifies a target (functional) feature. The T-Maps model for representing limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each of the contributing tolerances to the relationship. The method is to choose from a library of T-Maps the one that represents, in its own local (canonical) reference frame, each contributing feature and the tolerances specified on it; transform this T-Map to a coordinate frame centered at the target feature; obtain the accumulation T-Map for the assembly with the Minkowski sum; and fit a circumscribing functional T-Map to it. The fitting is accomplished numerically to determine the associated functional tolerance value. The sensitivity for each contributing tolerance-and-feature combination is determined by perturbing the tolerance, refitting the functional map to the accumulation map, and forming a ratio of incremental tolerance values from the two functional T-Maps. Perturbing the tolerance-feature combinations one at a time, the sensitivities for an entire stack of contributing tolerances can be built. For certain classes of loop equations, the same sensitivities result by fitting the functional T-Map to the T-Map for each feature, one-by-one, and forming the overall result as a scalar sum. Sensitivities help a designer to optimize tolerance assignments by identifying those tolerances that most strongly influence the dependent dimension at the target feature. Since the fitting of the functional T-Map is accomplished by intersection of geometric shapes, all the T-Maps are constructed with linear half-spaces.

Algebraic Representation of Geometric and Size Tolerances

1995 ◽  
Author(s):  
S. H. Mullins ◽  
D. C. Anderson
Keyword(s):  
Tolerance Analysis ◽  
Design Analysis ◽  
Algebraic Representation ◽  
Dimensional Metrology ◽  
Algebraic Form ◽  
Worst Case ◽  
Mechanical Component ◽  
Analysis And Synthesis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Abstract Presented is a method for mathematically modeling mechanical component tolerances. The method translates the semantics of ANSI Y14.5M tolerances into an algebraic form. This algebraic form is suitable for either worst-case or statistical tolerance analysis and seeks to satisfy the requirements of both dimensional metrology and design analysis and synthesis. The method is illustrated by application to datum systems, position tolerances, orientation tolerances, and size tolerances.

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